Plume virtual origin

A plume virtual origin is the extrapolated point at which a similarity plume's width and volume flux vanish. It absorbs finite source geometry into a shift of the axial coordinate.

For a horizontal forced plume, the plume virtual origin lies downstream and below the physical source on the far-field vertical asymptote. The origin shift in centreline arc length is distinct from its vertical height: if $z=s-D+o(1)$ and $\hat{s}=s+s_0$, the virtual height is $z_v=-D-s_0$. Both geometric shifts scale with the jet length at fixed entrainment coefficient.